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3249 bytes, as of the version from 2026-10-29 07:39 (current). Recorded here, not run.
# Argument selection for T603
This build applies both coordinated skill copies archived in
`agents/runs/20261029T070407Z-build-skills/manifest.json`. Both SHA-256 values
are `28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
This is the builder's justification; it is not an independent critique.
The named quantity is the zeta-regularized scalar Dirichlet Laplacian
determinant on a unit round hemisphere. The radius, boundary condition,
operator, lack of additive shift and zero-mode convention are fixed. The
family issue #240 was read before screening or computation. Its proposed
extent was reassessed against the archived skill rather than inherited as a
mandatory grid. The only free parameters are the following.
* `d`, type Z, category `discrete_index`: dimension indexes the established
geometric family H^d, for every integer d>=1. It changes both the eigenvalues
k(k+d-1) and their multiplicities binomial(d+k-2,d-1). Cunha–Freitas,
Section 3.1 and Theorem 3.2, and Dowker, Section 2, equations (1)–(3),
supply the family and conventions. We include every d from 1 through 20.
Twenty is a noncanonical practical cutoff, not a distinguished dimension.
This prefix retains the interval control, low-dimensional cases and ten
dimensions of each parity, without selecting only famous special cases.
Multiplicity degree at most 19 makes an independent continuation cheap.
The measured dry run has 40 entries, maximum 173 characters per full
working-precision ball, about 9 KB. The independent check takes less than
a second per dimension in this environment. These measurements justify
feasibility, not a need to extend to the source's 100-dimensional listing.
* `convention`, type Symbolic, category `intrinsic`: exhaustively `det`, then
`logdet`. These are the positive determinant and its natural logarithm,
with mutually inverse transformations exp and log. They index the same
quantity on identical dimension ranges, have comparable written lengths,
and convert cheaply. This is the skill's explicit invertible-convention
exception; it does not combine different boundary value problems.
The breadth review considered the unshifted geometric family, its odd and
even dimension formulas, and both canonical boundary conditions. Dirichlet
and Neumann define separate named spectral problems and therefore separate
tables; this build implements only Dirichlet. The full-sphere problem is
already T595 and is linked, not rebuilt. Variable cap angle, radius, mass and
curvature shift would introduce different families or continuous parameters
and are not hidden sampled choices here. No exploratory reference grid,
probability input or quantile is present. No claim of a separate documented
application is made for each dimension.
`generate.py` is self-contained and solely controls the selection. Its default
enumeration is d=1,...,20, `det` before `logdet`. The declaration describes
all positive dimensions, while `complete: no` and the completeness note state
the finite prefix and its rationale. The Programs range agrees. The critic
must independently inspect this selection and fingerprint the live generator;
this file supplies no acceptance decision or critique sidecar.